Gelation, which can occur when molecules react or colloids aggregate, is defined as the divergence of second and higher moments of molecular-weight and cluster-size distributions. Distribution kinetics and dynamics, described by population balance equations for aggregation and fragmentation, provide a framework for investigating quantitatively when and how gelation occurs and the conditions for existence of a nongelling steady state. We solve these integrodifferential equations for the size distribution by a numerical method and confirm the results by comparison with moment solutions. The results show how pregelation behavior is influenced by parameters in the aggregation and breakage kernels. (c) 2007 Elsevier Ltd. All rights reserved.